{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "## 3d 目标检测 判断点云是否在bbox中\n",
    "* 参考：https://blog.csdn.net/qq_35632833/article/details/106865648\n",
    "\n",
    "https://www.yuque.com/huangzhongqing/ai_meeting/vn11kw#WWcAx\n"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.collections import PolyCollection, LineCollection # 可视化\n",
    "from scipy.spatial import Delaunay\n",
    "\n",
    "lidar_file = \"/home/hcq/huituo_server/data/kitti/training/velodyne/000000.bin\" # 文件路径\n",
    "pts = np.fromfile(lidar_file, dtype=np.float32).reshape(-1, 4)\n",
    "# print(\"原始点：\", pts)\n",
    "print(\"原始点shape：\",pts.shape)\n",
    "# 判断 Test if points in `p` are in `hull`\n",
    "def in_hull(p, hull):\n",
    "    \"\"\"\n",
    "    Test if points in `p` are in `hull`\n",
    "\n",
    "    `p` should be a `NxK` coordinates of `N` points in `K` dimensions\n",
    "    `hull` is either a scipy.spatial.Delaunay object or the `MxK` array of the \n",
    "    coordinates of `M` points in `K`dimensions for which Delaunay triangulation\n",
    "    will be computed\n",
    "    \"\"\"\n",
    "    from scipy.spatial import Delaunay\n",
    "    if not isinstance(hull,Delaunay):\n",
    "        hull = Delaunay(hull)\n",
    "\n",
    "    return hull.find_simplex(p)>=0, hull.find_simplex(p) < 0\n",
    "\n",
    "# 可视化\n",
    "def plot_in_hull(p, hull):\n",
    "    \"\"\"\n",
    "    plot relative to `in_hull` for 2d data\n",
    "    \"\"\"\n",
    "    if not isinstance(hull,Delaunay):\n",
    "        hull = Delaunay(hull)\n",
    "\n",
    "    # plot triangulation 可视化的第一张图\n",
    "    poly = PolyCollection(hull.points[hull.vertices], facecolors='w', edgecolors='b') # 蓝色那条线\n",
    "    plt.clf()\n",
    "    plt.title('in hull') # 标题\n",
    "    plt.gca().add_collection(poly)\n",
    "    # plt.plot(hull.points[:,0], hull.points[:,1], 'o', hold=1)\n",
    "    plt.plot(hull.points[:,0], hull.points[:,1], 'o')  \n",
    "\n",
    "\n",
    "    # plot the convex hull\n",
    "    edges = set()\n",
    "    edge_points = []\n",
    "\n",
    "    def add_edge(i, j):\n",
    "        \"\"\"Add a line between the i-th and j-th points, if not in the list already\"\"\"\n",
    "        if (i, j) in edges or (j, i) in edges:\n",
    "            # already added\n",
    "            return\n",
    "        edges.add( (i, j) )\n",
    "        edge_points.append(hull.points[ [i, j] ])\n",
    "\n",
    "    for ia, ib in hull.convex_hull:\n",
    "        add_edge(ia, ib) # 凸包\n",
    "    # 第1张图\n",
    "    lines = LineCollection(edge_points, color='g') # 绿线\n",
    "    plt.gca().add_collection(lines)\n",
    "    plt.show()    \n",
    "\n",
    "\n",
    "    # 第2张图\n",
    "    # plot tested points `p` - black are inside hull, red outside  黑色内点，红色外点\n",
    "    inside, out = in_hull(p,hull) # 将所有点分为内点和外点   \n",
    "    plt.plot(p[inside,0],p[inside,1],'.k') # 黑色\n",
    "    plt.plot(p[out,0],p[out,1],'.r') # 添加红色\n",
    "    # plt.plot(p[-inside,0],p[-inside,1],'.r')\n",
    "    plt.show()\n",
    "\n"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "原始点shape： (115384, 4)\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "source": [
    "if __name__ == '__main__':\n",
    "    \n",
    "    p1 = pts[2000,0:2]\n",
    "    p2 = pts[12782,0:2]\n",
    "    p3 = pts[48772,0:2]\n",
    "    p4 = pts[38217,0:2] # 四个(x,y )点\n",
    "\n",
    "    p_in = np.vstack((p1, p2, p3, p4))\n",
    "    plot_in_hull(pts[:,0:2], p_in)  # 可视化前面两个图\n",
    "\n",
    "\n",
    "    # 方法 2 \n",
    "    import pylab\n",
    "    import numpy\n",
    "    from scipy.spatial import ConvexHull\n",
    "\n",
    "    def is_p_inside_points_hull(points, p):\n",
    "        global hull, new_points # Remove this line! Just for plotting!\n",
    "        hull = ConvexHull(points)\n",
    "        new_points = numpy.append(points, p, axis=0) # 对待判定的每个点，逐一加入原有点集\n",
    "        new_hull = ConvexHull(new_points) # 新的hull点\n",
    "        if list(hull.vertices) == list(new_hull.vertices): # 判断新形成的凸包的边界点集是否有改变\n",
    "            return True\n",
    "        else:\n",
    "            return False\n",
    "\n",
    "    # Test:\n",
    "    # points = numpy.random.rand(10, 2)   # 30 random points in 2-D\n",
    "    # # Note: the number of points must be greater than the dimention.\n",
    "    # p = numpy.random.rand(1, 2) # 1 random point in 2-D\n",
    "\n",
    "    points = pts[:,0:2]\n",
    "    p = np.vstack((p1, p2, p3, p4))\n",
    "\n",
    "    print(\"is_p_inside_points_hull\", is_p_inside_points_hull(points, p)) # 输出\n",
    "\n",
    "    # Plot:可视化\n",
    "    pylab.plot(points[:,0], points[:,1], 'o') # 所有点\n",
    "    for simplex in hull.simplices:\n",
    "        pylab.plot(points[simplex,0], points[simplex,1], 'k-')  # 所有点的边界线\n",
    "    pylab.plot(p[:,0], p[:,1], '^r') # 那四个红点\n",
    "    pylab.show()\n"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "is_p_inside_points_hull True\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [],
   "outputs": [],
   "metadata": {}
  }
 ],
 "metadata": {
  "orig_nbformat": 4,
  "language_info": {
   "name": "python",
   "version": "3.6.12",
   "mimetype": "text/x-python",
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "pygments_lexer": "ipython3",
   "nbconvert_exporter": "python",
   "file_extension": ".py"
  },
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3.6.12 64-bit ('common': conda)"
  },
  "interpreter": {
   "hash": "23f77d03b5a41e4d3ddb9e0caaaf52efc8b96489adee7c10c83419330a6f57cc"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}